How much heat i released to the environment as 245 g of steam at 140°C is cooled to -15°C?

Question

Henry Antrim · Accepted Answer

Warning! Long answer! The process releases 765 kJ of heat into the environment.

In this problem, five distinct heats are involved: Q_1 + q_2 + q_3 + q_4 + q_5# = #q #= mc_1ΔT_1 + mΔ_text(cond)H + mc_3ΔT_3 + mΔ_text(fus)H + mc_5ΔT_5# where Heats #q_1, q_2, q_3, q_4,#, and #q_5# are associated with each step. #m# is the sample's mass. T_"f" -T_"i"# = #ΔT "the enthalpy of condensation of steam" = "-2258 J·g"^"-1"#Ô_text(cond)H "the enthalpy of solidification of water" = "-333.55 J·g"^"-1"#Δ_text(sol)H #bbq_1# #ΔT_1 = "100°C - 140°C" = "-40°C"# mc_1ΔT_1 = 245 color(red)(cancel(black)("g"))) × 2.010 color(white)(l)"J"·color(red)(cancel(black)("°C"^"-1""g"^"-1"))) × ("-40") color(red)(cancel(black)("°C"))) = "-19 700 J"# #bbq_2# #q_2 = 245 × ("-2258")color(white)(l) "J"·color(red)(cancel(color(black)("g"^"-1"))) = "-553 200 kJ"# #bbq_3# #ΔT = "-100°C" = "0°C - 100°C"# mcΔT = 245 color(red)(cancel(black)("g"))) × 4.184 color(white)(l)"J"·color(red)(cancel(black)( "°C"^"-1""g"^"-1"))) × ("-100") color(red)(cancel(black)("°C"))) = "-102 500 J"# #grill_4# #q_4 = 245 color(black)(cancel(color(red)("g"))) × ("-333.55")color(white)(l) "J"·color(black)(cancel(color(red)("g"^"-1"))) = "-81 720 kJ"# #bbq_5# "-15 °C - 0 °C" = "-15 °C"# #ΔT_5 Q_5 = mcΔT = 245 color(red)(cancel(black)("g"))) × 2.010 color(white)(l)"J"·color(red)(cancel(black)("°C"^"-1""g"^"-1"))) × ("-15") color(red)(cancel(black)("°C"))) = "-7390 J"# #= "-19 700 J" - "553 200 J" - "102 500 J" - "81 720 J" - "7390 J" = "-765 000 J" = "-765 kJ"# 765 kJ of heat are released into the atmosphere during the process.

Owen Ambrose · Answer

undefined To calculate the heat released, you can use the formula:

$$Q = mcΔT$$

Where:
- $Q$ is the heat released,
- $m$ is the mass of the substance (in grams),
- $c$ is the specific heat capacity of the substance (for water, it's 4.18 J/g°C),
- $ΔT$ is the change in temperature (initial temperature - final temperature).

First, you need to find the initial temperature of the steam in Celsius by converting it from 140°C to Kelvin, then find the heat released using the formula above.